Average Error: 0.0 → 0.0
Time: 18.9s
Precision: 64
\[\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)\]
↓
\[\sqrt[3]{\left(\left(\frac{\sqrt{1 - 3 \cdot \left(v \cdot v\right)}}{\frac{4}{\sqrt{2}}} \cdot \left(1 - v \cdot v\right)\right) \cdot \left(\frac{\sqrt{1 - 3 \cdot \left(v \cdot v\right)}}{\frac{4}{\sqrt{2}}} \cdot \left(1 - v \cdot v\right)\right)\right) \cdot \left(\frac{\sqrt{1 - 3 \cdot \left(v \cdot v\right)}}{\frac{4}{\sqrt{2}}} \cdot \left(1 - v \cdot v\right)\right)}\]
\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)
↓
\sqrt[3]{\left(\left(\frac{\sqrt{1 - 3 \cdot \left(v \cdot v\right)}}{\frac{4}{\sqrt{2}}} \cdot \left(1 - v \cdot v\right)\right) \cdot \left(\frac{\sqrt{1 - 3 \cdot \left(v \cdot v\right)}}{\frac{4}{\sqrt{2}}} \cdot \left(1 - v \cdot v\right)\right)\right) \cdot \left(\frac{\sqrt{1 - 3 \cdot \left(v \cdot v\right)}}{\frac{4}{\sqrt{2}}} \cdot \left(1 - v \cdot v\right)\right)}
double f(double v) {
        double r6371142 = 2.0;
        double r6371143 = sqrt(r6371142);
        double r6371144 = 4.0;
        double r6371145 = r6371143 / r6371144;
        double r6371146 = 1.0;
        double r6371147 = 3.0;
        double r6371148 = v;
        double r6371149 = r6371148 * r6371148;
        double r6371150 = r6371147 * r6371149;
        double r6371151 = r6371146 - r6371150;
        double r6371152 = sqrt(r6371151);
        double r6371153 = r6371145 * r6371152;
        double r6371154 = r6371146 - r6371149;
        double r6371155 = r6371153 * r6371154;
        return r6371155;
}
↓
double f(double v) {
        double r6371156 = 1.0;
        double r6371157 = 3.0;
        double r6371158 = v;
        double r6371159 = r6371158 * r6371158;
        double r6371160 = r6371157 * r6371159;
        double r6371161 = r6371156 - r6371160;
        double r6371162 = sqrt(r6371161);
        double r6371163 = 4.0;
        double r6371164 = 2.0;
        double r6371165 = sqrt(r6371164);
        double r6371166 = r6371163 / r6371165;
        double r6371167 = r6371162 / r6371166;
        double r6371168 = r6371156 - r6371159;
        double r6371169 = r6371167 * r6371168;
        double r6371170 = r6371169 * r6371169;
        double r6371171 = r6371170 * r6371169;
        double r6371172 = cbrt(r6371171);
        return r6371172;
}

Error

Bits error versus v

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)\]
  2. Using strategy rm

  3. Applied add-cbrt-cube0.0

    \[\leadsto \left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \color{blue}{\sqrt[3]{\left(\left(1 - v \cdot v\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \left(1 - v \cdot v\right)}}\]

  4. Applied add-cbrt-cube0.0

    \[\leadsto \color{blue}{\sqrt[3]{\left(\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right)\right) \cdot \left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right)}} \cdot \sqrt[3]{\left(\left(1 - v \cdot v\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \left(1 - v \cdot v\right)}\]

  5. Applied cbrt-unprod0.0

    \[\leadsto \color{blue}{\sqrt[3]{\left(\left(\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right)\right) \cdot \left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right)\right) \cdot \left(\left(\left(1 - v \cdot v\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \left(1 - v \cdot v\right)\right)}}\]

  6. Simplified0.0

    \[\leadsto \sqrt[3]{\color{blue}{\left(\left(\left(1 - v \cdot v\right) \cdot \frac{\sqrt{1 - 3 \cdot \left(v \cdot v\right)}}{\frac{4}{\sqrt{2}}}\right) \cdot \left(\left(1 - v \cdot v\right) \cdot \frac{\sqrt{1 - 3 \cdot \left(v \cdot v\right)}}{\frac{4}{\sqrt{2}}}\right)\right) \cdot \left(\left(1 - v \cdot v\right) \cdot \frac{\sqrt{1 - 3 \cdot \left(v \cdot v\right)}}{\frac{4}{\sqrt{2}}}\right)}}\]

  7. Final simplification0.0

    \[\leadsto \sqrt[3]{\left(\left(\frac{\sqrt{1 - 3 \cdot \left(v \cdot v\right)}}{\frac{4}{\sqrt{2}}} \cdot \left(1 - v \cdot v\right)\right) \cdot \left(\frac{\sqrt{1 - 3 \cdot \left(v \cdot v\right)}}{\frac{4}{\sqrt{2}}} \cdot \left(1 - v \cdot v\right)\right)\right) \cdot \left(\frac{\sqrt{1 - 3 \cdot \left(v \cdot v\right)}}{\frac{4}{\sqrt{2}}} \cdot \left(1 - v \cdot v\right)\right)}\]

Reproduce

herbie shell --seed 2019133 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 2"
  (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))))